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Properties of the slant weighted Toeplitz operator. (English) Zbl 1219.47046
Summary: If $\beta ={〈\beta 〉}_{n\in ℤ}$ is a sequence of positive numbers, then a slant weighted Toeplitz operator ${A}_{\varphi }$ is an operator on ${L}^{2}\left(\beta \right)$ defined as ${A}_{\varphi }=W{M}_{\varphi }$, where ${M}_{\varphi }$ is the multiplication operator on ${L}^{2}\left(\beta \right)$. When the sequence $\beta \equiv 1$, this operator reduces to the ordinary slant Toeplitz operator given by M. C. Ho [Indiana Univ. Math. J. 45, No. 3, 843–862 (1996; Zbl 0880.47016)]. In this paper, we study some algebraic properties of a slant weighted Toeplitz operator. We also obtain its matrix characterization and discuss the adjoint of this operator.
##### MSC:
 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators